Abstract
In this short paper, I selectively review some recent developments related to the idea that jumps in stock prices incorporate the most valuable information, and thus the quantification of a stock’s exposure to jump events is important for financial risk management and portfolio construction. There are two main methodologies of estimating jump betas: a) the more widely used high or ultra high frequency procedures that rely on the asymptotical behavior of elaborate and sophisticated econometric constructs, such as the bi-power variation or local averaging techniques in order to isolate market microstructure noise at high frequencies, and b) very recently a new non-parametric skew-based methodology that does not rely on the use of high frequency data and is thus immune to market microstructure noise.
Highlights
The use of diffusion based asset pricing theories in pricing real world financial assets presents a major challenge for economists and financial experts
One of the reasons of such difficulty in fitting real stock return and option price data to most models is that real prices seem to exhibit exposure to extreme moves and asymmetry in ways that do not seem easy to comprehend
Evidence of jumps that help better explain the higher moments of asset returns, namely excess kurtosis and skew, is widely recognized
Summary
The use of diffusion based asset pricing theories in pricing real world financial assets presents a major challenge for economists and financial experts. One of the reasons of such difficulty in fitting real stock return and option price data to most models is that real prices seem to exhibit exposure to extreme moves (excess kurtosis) and asymmetry (skew) in ways that do not seem easy to comprehend In such an environment an investor who exhibits skew preference can improve the mean-variance profile of an asset by “selling” its return skew either through dynamic trading or using option based strategies. Theories that incorporated discontinuity and fat tails in price dynamics mainly focused on the implications of exposure to significant events (so called “peso” moments); that is large but infrequent jumps that are clearly identified breaks in the price process Even though such jump diffusion models can correctly incorporate extreme events at a macroeconomic level, their assumed low jump activity cannot suitably capture discontinuity of a more frequent and continuously present nature. I review two methodologies of estimating jump betas a) the more widely used high frequency procedures, and b) a simple skew-based methodology
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